4th Grade Adding and Subtracting Fractions and Mixed Numbers Test Answer Key and Scoring Guide (PDF)

$4th grade adding fractions test answer key – Maths PDF$

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This 4th grade adding fractions test answer key covers adding and subtracting fractions and mixed numbers (Common Core 4.NF.B.3a, 4.NF.B.3b, 4.NF.B.3c, 4.NF.B.3d), with a free PDF to print.

Key takeaway: This answer key helps fourth grade students see how each point on the fractions test was earned.

Topic: Adding and Subtracting Fractions and Mixed Numbers (4th grade)
Content: Worked solutions and a scoring guide for 9 questions
Standards: 4.NF.B.3a, 4.NF.B.3b, 4.NF.B.3c, 4.NF.B.3d
Answers: Every step shown, with the method to review
Format: Free printable PDF, US Letter, black and white

This answer key helps fourth grade students see how each point on the fractions test was earned. Also, it gives full solutions to all nine questions, including the conversions in questions 3 and 4 and the three part word problems in questions 7 and 8.

Each solution keeps the denominator visible and explains any regrouping in words. Then, question 2 lists more than one correct decomposition of $\frac{7}{8}$, and question 9 explains why adding denominators is wrong. Add up your points out of 20, then spend about 15 minutes redoing every question that lost credit on a fresh sheet of paper.

Use this answer key and scoring guide to grade the fractions test. Each solution shows the steps, and the scoring notes explain how partial credit is awarded out of 20 points.

Grade 4 · Common Core State Standards: 4.NF.B.3a, 4.NF.B.3b, 4.NF.B.3c, 4.NF.B.3d

4th grade adding fractions test answer key: worked solutions

1 – Like denominators [2 pts]

(a) $3 + 6 = 9$. (b) $11 – 4 = 7$.

(a) $\frac{9}{10}$ (b) $\frac{7}{12}$

Scoring: 1 point for each correct answer; 0 points if the denominator is added.

2 – Decompose [2 pts]

Split 7 into 3 + 4 and 5 + 2.

One way to decompose.

$\frac{7}{8} = \frac{3}{8} + \frac{4}{8}$ and $\frac{7}{8} = \frac{5}{8} + \frac{2}{8}$ (other correct splits are accepted)

Scoring: 1 point for each correct decomposition.

3 – Mixed number picture [2 pts]

2 whole strips and 3 fifths: $2\frac{3}{5}$.

$2 = \frac{10}{5}$, and $\frac{10}{5} + \frac{3}{5} = \frac{13}{5}$.

$2\frac{3}{5}$ = $\frac{13}{5}$

Also, Scoring: 1 point for the mixed number; 1 point for the improper fraction.

4 – Convert [2 pts]

(a) $17 \div 6 = 2$ remainder 5, so $2\frac{5}{6}$.

(b) $3 = \frac{6}{2}$, and $\frac{6}{2} + \frac{1}{2} = \frac{7}{2}$.

(a) $2\frac{5}{6}$ (b) $\frac{7}{2}$

Scoring: 1 point for each part.

5 – Add mixed numbers [2 pts]

Wholes: $2 + 3 = 5$. Fractions: $\frac{5}{8} + \frac{6}{8} = \frac{11}{8} = 1\frac{3}{8}$.

$5 + 1\frac{3}{8} = 6\frac{3}{8}$.

$6\frac{3}{8}$

Scoring: 1 point for adding the wholes and the fractions; 1 point for regrouping to the correct answer.

Question 6 and after

6 – Subtract mixed numbers [2 pts]

$6\frac{2}{5} = \frac{32}{5}$ and $3\frac{4}{5} = \frac{19}{5}$.

$\frac{32}{5} – \frac{19}{5} = \frac{13}{5} = 2\frac{3}{5}$.

$2\frac{3}{5}$

Scoring: 1 point for converting correctly; 1 point for the correct answer.

7 – Hiking trail [3 pts]

(a) $5\frac{2}{10} = \frac{52}{10}$ and $2\frac{7}{10} = \frac{27}{10}$. $\frac{52}{10} – \frac{27}{10} = \frac{25}{10} = 2\frac{5}{10}$.

The part left is 2 $\frac{5}{10}$ miles.

(b) $2\frac{5}{10} = \frac{25}{10}$ and $1\frac{8}{10} = \frac{18}{10}$. $\frac{25}{10} – \frac{18}{10} = \frac{7}{10}$.

(a) $2\frac{5}{10}$ miles (b) $\frac{7}{10}$ mile

Scoring: (a) 1 point for the method, 1 point for the answer; (b) 1 point.

8 – Farmers market [3 pts]

(a) Wholes $1 + 2 = 3$, fractions $\frac{3}{4} + \frac{2}{4} = \frac{5}{4} = 1\frac{1}{4}$, so $4\frac{1}{4}$.

(b) $4\frac{1}{4} + \frac{3}{4} = 4\frac{4}{4} = 5$.

(a) $4\frac{1}{4}$ lb (b) 5 lb (c) 1 lb

Scoring: 1 point for each part.

9 – Mia's mistake [2 pts]

Mia added the denominators. The size of the parts (fifths) does not change when you add. Two fifths plus two fifths is four fifths.

$\frac{2}{5} + \frac{2}{5} = \frac{4}{5}$

Scoring: 1 point for the explanation; 1 point for the correct sum.

Total score

Total

20 points

Key facts behind this 4th grade adding fractions test answer key

Key facts

With like denominators, add or subtract the numerators and keep the denominator.
Next, a fraction can be decomposed in more than one way, such as 5/6 = 2/6 + 3/6.
A mixed number such as 2 1/4 equals the improper fraction 9/4.
Then, to add mixed numbers, add the wholes and the fractions, then regroup when the fraction is greater than 1.
To subtract mixed numbers, change them to improper fractions first.

Common mistakes with this 4th grade adding fractions test answer key

Students assume their decomposition in question 2 is wrong if it differs from the key. Instead, add your two fractions and see whether they make $\frac{7}{8}$.
Students miss part credit by writing only a final answer in question 7. Parts are scored separately, so each needs a line of work.
Students read the explanation of Mia’s mistake and then repeat it later. Also, say aloud why $\frac{2}{5} + \frac{2}{5}$ stays in fifths before moving on.
Students compare question 5 only by the final number. Check that the fraction part was regrouped into a whole, since the sum of eighths is more than 1.

How to learn from your test

Group your missed questions by skill, such as converting, adding mixed numbers, or word problems. Then practice the weakest group first.
Use the point values to find where the most credit was lost. Questions 7 and 8 together are worth 6 points, so they are worth another look.
Teachers can ask students to trade tests and explain one correction to a partner. Then, teaching a fix is a strong way to remember it.

Download the 4th grade adding fractions test answer key as a PDF with the button below and keep it with your notes.

4th grade adding fractions test answer key: frequently asked questions

Why can question 2 have many correct answers?

A fraction can be split into parts in more than one way. For $\frac{7}{8}$, the numerators of the two parts only need to add to 7, so $\frac{3}{8} + \frac{4}{8}$ and $\frac{1}{8} + \frac{6}{8}$ are both correct. So, check by adding.

How do you convert 17/6 to a mixed number?

Divide 17 by 6. Also, the quotient 2 is the whole number part, and the remainder 5 becomes the numerator. So $\frac{17}{6} = 2\frac{5}{6}$. You can check by multiplying $2 \times 6 = 12$, adding 5, and seeing 17 again.

What if I made a small arithmetic slip but used the right method?

Most teachers give partial credit when the method is correct. Mark the slip, redo that step, and note what went wrong. Slips with carries or regrouping are common, and the add-back check can catch them before you turn in a test.

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